CN102545987B - A Multi-cell Adaptive Cooperative Transmission Method Based on Delay Feedback - Google Patents

Abstract

The invention discloses a multicell self-adaption cooperative transmission method on the basis of delayed feedback. The cooperative transmission method is carried out according to the following steps: firstly, an average movement speed of users in a plurality of cells which take part in cooperation is researched, a corresponding doppler frequency offset is calculated and a channel delay correlation coefficient is obtained; then one user is selected from each cell by round-robin scheduling to wait for data transmission and a codebook known by a base station end is generated for the user; the user estimates channel information and a path power attenuation factor by receiving a pilot signal sent by a base station and feeds back the information to the base station; and finally, the base station determines an adopted cooperative transmission mode according to the information fed back by the user and information of the calculated channel delay correlation coefficient and the like, completes precoding in a corresponding mode and carries out data transmission. The multicell self-adaption cooperative transmission method can be effectively applied to actual scenes and the reachable transmission speed and the frequency spectrum utilization rate of a system can be improved.

Description

A Multi-cell Adaptive Cooperative Transmission Method Based on Delay Feedback

technical field

The invention relates to an adaptive cooperative transmission method in a multi-cell environment, and belongs to the field of cooperative transmission in a multiple-input multiple-output (MIMO) system in a multi-cell environment.

Background technique

At present, in the case of increasingly tight wireless resources, in a multi-cell environment, the use of multi-antenna and global frequency reuse technology can fully tap and utilize space resources, and maximize spectrum utilization and power efficiency. However, co-frequency coverage will inevitably lead to significant Inter-Cell Interference (ICI), and the resulting performance degradation of cell-edge users has become an increasingly prominent problem, seriously restricting the further improvement of the system's achievable transmission rate. In order to cope with this challenge, in recent years, some scholars have continuously proposed that the cooperation of multiple base stations in adjacent cells can be used to suppress inter-cell interference and improve the reachable rate of the system.

In the prior art, there are two effective cooperation modes that attract people's attention, namely joint processing mode (JP) and cooperative beamforming mode (CBF). In the JP cooperation mode, in a transmission time slot, multiple base stations participating in the cooperation perform joint data transmission to a scheduled user at the same time, and select different users for transmission in different time slots. In the CBF cooperation mode, in all transmission time slots, each base station is only responsible for data transmission to the scheduled users in its own cell, and uses the shared channel information to suppress interference for users in adjacent cells. The difference between the two cooperation modes is that in the JP cooperation mode, the base stations participating in the cooperation not only need to share the channel information fed back by the user to the main base station, but also need to share the data information sent by the base station to the user; while in the CBF cooperation mode, the participating base stations need to share The base station only needs to share the channel information that the user feeds back to its main base station, so the data sharing load is significantly reduced, and the system delay is also reduced accordingly. The two cooperation modes can obtain different system achievable rates in different application scenarios, so an actual system can switch between the two modes to achieve maximum rate transmission.

The existing CBF and JP mode evaluation schemes are all based on the assumption that the base station can obtain the ideal channel information, but in actual application scenarios, whether it is a time division duplex (TDD) or a frequency division duplex (FDD) system, this It is difficult to satisfy any assumption. If the system adopts time division duplex (TDD), the transmitter can estimate the uplink channel information at the base station and use it as the downlink channel information through the principle of mutuality, but the uplink and downlink are not completely symmetrical , so there is inevitably an estimation error in the channel information obtained by the base station through reciprocity. If the system adopts frequency division duplex (FDD), the downlink channel information is usually estimated by the user terminal, and then the user feeds back the downlink channel information to the base station through the feedback link, but the amount of information that the user can feedback in the actual system is limited. In order to meet the capacity requirements of the feedback link, the user often quantizes the channel information first, then feeds the quantized information back to the base station through limited bits, and finally the base station recovers the channel information as much as possible based on the feedback information. This solution will lead to a certain quantization error between the system channel information obtained by the base station and the real channel information, and the size of the quantization error is determined by the capacity of the feedback link. In addition, when the feedback mechanism is used, there is an information delay problem caused by the feedback link, that is, the feedback information obtained by the base station is not the channel information at the current moment, but the channel information before a certain delay. Under the influence of the above factors, the downlink information obtained by the base station does not completely match the real channel information, resulting in a significant decline in the performance of the adaptive transmission scheme based on ideal channel information. Under the condition of channel information, the problem of adaptive switching between JP and CBF cooperative modes.

Contents of the invention

Purpose of the invention: In order to overcome the deficiencies in the prior art, the present invention provides a multi-cell adaptive cooperative transmission method based on delay feedback when the base station can only obtain feedback channel information with limited delay.

Technical solution: In order to achieve the above purpose, the present invention proposes a multi-cell adaptive cooperative transmission method based on delay feedback. The cooperative transmission method is carried out as follows: first investigate the average moving rate of users in the multi-cell participating in the cooperation, and calculate Calculate the corresponding Doppler frequency offset, obtain the channel delay correlation coefficient, and then select a user in each cell to wait for data transmission through round-robin scheduling, and generate a codebook known by the base station for the user, and then the user passes Receive the pilot signal sent by the base station, estimate the channel information and path power attenuation factor, and feed these information back to the base station, and finally the base station determines the cooperative transmission mode adopted according to the information fed back by the user and the calculated channel delay correlation coefficient and other information , complete the precoding in the corresponding mode, and perform data transmission. The present invention provides a method for realizing adaptive cooperative transmission in a multi-cell system when the channel information obtained by the base station has non-ideal factors such as quantization error, feedback delay, and path power loss, and the method can be effectively applied in practice In the scenario, it can effectively improve the achievable transmission rate and spectrum utilization of the system.

Specifically, the cooperative transmission method of the present invention is carried out according to the following steps:

(1) The system surveys the average moving speed v of multiple user terminals in the M adjacent cells participating in the cooperation, 2≤M≤7, and calculates the user's Doppler frequency offset f _d =f _c v/c, according to Clark ( Clarke) scattering model calculates the channel delay correlation coefficient ρ=J ₀ (2πf _d T _s ), where c represents the speed of light, f _c represents the carrier frequency, T _s represents the length of each symbol period, and J ₀ (·) represents Zero-order Bessel functions of the first kind;

(2) Each cell selects a user to wait for data transmission through round-robin scheduling. At the beginning of each transmission, the user first performs channel estimation to obtain channel information and path power attenuation factor, and then quantizes the channel information according to the existing codebook. Feedback the quantized channel information and the path power attenuation factor to the base station;

(3) The base station compares the two alternative modes, namely the coordinated beamforming mode (CBF) and the joint processing mode (JP), according to the feedback channel information, the path power attenuation factor and the Doppler frequency offset, and determines that the system adopts cooperative transmission mode;

(4) The base station calculates the precoding matrix W by using the delayed feedback channel information according to the selected transmission mode, and then multiplies the data to be sent by the precoding matrix W to perform data transmission.

Based on the analysis of various non-ideal factors such as quantization error, feedback delay and path power loss in the actual system, the achievable transmission rate of the system under the two cooperative modes of cooperative beamforming mode and joint processing mode is respectively given. Closed solution R _CBF and R _JP , and based on the closed solution, adaptively select the cooperation mode for data transmission:

(1) Calculate the achievable transmission rates R _CBF and R _JP of the system in the cooperative beamforming mode and the joint processing mode respectively,

1) In the cooperative beamforming mode, the closed-form solution of the achievable transmission rate R _CBF of the system is:

${\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; CBF</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; log</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; e</span>}<span\; class="notranslate">\; )</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}}{\overset{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}<span\; class="notranslate">\; [</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; )</span>}\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; !</span>{<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; \&mu;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{{\mathrm{<span\; class="notranslate">\; \&mu;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; \&mu;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}<span\; class="notranslate">\; ,</span>\frac{{\mathrm{<span\; class="notranslate">\; \&mu;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{{\mathrm{<span\; class="notranslate">\; \&mu;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span>$

其中P表示M个基站总的发射功率，2≤M≤7，α，β分别表示基站到本小区用户和相邻小区用户的路径功率衰减因子，B表示反馈比特数，N_t表示每个基站上发射天线的数量，N_t≤8，

ρ表示信道延时相关系数，同时，In the formula, μ ₁ =αP/M, μ ₂ =βP/M,

Among them, P represents the total transmission power of M base stations, 2≤M≤7, α and β represent the path power attenuation factors from the base station to the users in this cell and users in adjacent cells, respectively, B represents the number of feedback bits, and N _t represents each base station The number of transmitting antennas, N _t ≤ 8,

ρ represents the channel delay correlation coefficient, and at the same time,

${\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; !</span>}{<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}\frac{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; !</span>}{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; !</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; !</span>}{<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; i</span>}}$

${\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; !</span>}{<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}\frac{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; !</span>}{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; !</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; !</span>}{<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; i</span>}}$

The closed form solution of I( , , ) is given by:

$\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 1,1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{<span\; class="notranslate">\; (</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; )</span>}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$

where I ₀ ( , , ) is given by:

${\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\left\{\begin{array}{cc}{\mathrm{<span\; class="notranslate">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; ab</span>}}{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; ab</span>}<span\; class="notranslate">\; )</span>& \mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>\\ \frac{{<span\; class="notranslate">\; (</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; !</span>}{\mathrm{<span\; class="notranslate">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; ab</span>}}{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; ab</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\frac{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; !</span>{<span\; class="notranslate">\; (</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>{<span\; class="notranslate">\; !</span>\mathrm{<span\; class="notranslate">\; b</span>}}^{\mathrm{<span\; class="notranslate">\; k</span>}}}& \mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; \&Greater\; Equal;</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; .</span>\end{array}\right.$

In the formula ${\mathrm{E.}}_1\left(a\right)={\&Integral;}_1^{\&infin;}{t}^{-1}{e}^{-\mathrm{at}}\mathrm{dt},$ is the first-order exponential integral function.

2) In the joint processing mode, the closed-form solution of the achievable transmission rate R _JP of the system is:

${\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; JP</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; log</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&gamma;\; l</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; ln</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; l</span>}}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; 3</span>}\mathrm{<span\; class="notranslate">\; l</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 2</span>}}{{\mathrm{<span\; class="notranslate">\; 15</span>}\mathrm{<span\; class="notranslate">\; l</span>}}^{\mathrm{<span\; class="notranslate">\; 4</span>}}}<span\; class="notranslate">\; )</span>$

γ and l are given by:

$\mathrm{<span\; class="notranslate">\; \&gamma;</span>}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; ,</span>$ $\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}$

In the formula,

${\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="N\; t\; c"\; filenames="HDA0000131155990000022.png"\; state="\{\{state\}\}">N</figure-callout></span><figure-callout\; id="1"\; label="N\; t\; c"\; filenames="HDA0000131155990000022.png"\; state="\{\{state\}\}">\; </figure-callout>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}{}_{}^{}{\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="c"\; filenames="HDA0000131155990000022.png"\; state="\{\{state\}\}">c</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}{\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}$

A ₂ ＝1+c ₁ N _t +c ₂ +c ₃ (M-1)N _t +c ₄ (M-1)

Among them, c ₁ , c ₂ , c ₃ , and c ₄ are the corresponding constant correction items, and the calculation formula is as follows:

${\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="c"\; filenames="HDA0000131155990000022.png"\; state="\{\{state\}\}">c</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; \&alpha;\&zeta;P</span>}}{\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}$ ${\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="c"\; filenames="HDA0000131155990000022.png"\; state="\{\{state\}\}">c</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; \&alpha;P</span>}}{\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}_{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="e"\; filenames="HDA0000131155990000022.png"\; state="\{\{state\}\}">e</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}$

${\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; \&beta;\&zeta;P</span>}}{\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}$ ${\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; \&beta;P</span>}}{\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}_{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="e"\; filenames="HDA0000131155990000022.png"\; state="\{\{state\}\}">e</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}$

In the formula, $\mathrm{\&zeta;}=1-2^B\&CenterDot;\mathrm{\&beta;}(2^B,\frac{N_t}{N_t-1}).$ $\mathrm{\&beta;}(x,\mathrm{the\; y})={\&Integral;}_0^1{t}^{x-1}{(1-t)}^{\mathrm{the\; y}-1}\mathrm{dt},$ is the Beta function.

的第j列，其中

表示伪逆，

表示基站j到M个用户的反馈信道信息，2≤M≤7；(2) If R _CBF ≥ R _JP is satisfied, select the cooperative beamforming mode (CBF) cooperative mode. In this mode, the precoding matrix W of base station j is

The jth column of , where

represents the pseudo-inverse,

Indicates the feedback channel information from base station j to M users, 2≤M≤7;

其中

表示基站j到用户k的反馈信道信息。If R _JP >R _CBF is satisfied, the joint processing mode (JP) cooperation mode is selected. In this mode, the precoding matrix W of base station j is

in

Indicates the feedback channel information from base station j to user k.

Beneficial effects: Compared with the prior art, a delayed feedback-based multi-cell adaptive cooperative transmission method of the present invention has the following advantages:

(1) Compared with the ideal situation in which the base station is assumed to know accurate channel information, the present invention can effectively resist the performance deterioration caused by non-ideal factors such as quantization error, feedback delay and path power loss in the actual system, thereby obtaining higher System transfer rate;

(2) The invention adopts the zero-forcing beamforming (ZFBF) precoding scheme in the CBF cooperation mode, and adopts the local precoding scheme in the JP cooperation mode (that is, directly uses the feedback channel information as the precoding matrix), and realizes low complexity , and better system performance can be obtained.

Description of drawings

Fig. 1 is a system block diagram of the multi-cell adaptive cooperative transmission method based on delay feedback proposed by the present invention;

Figure 2 is a diagram of the relationship between the feasible domain of the two cooperation modes and the change of the transmission signal-to-noise ratio and the Doppler frequency offset in the case of different feedback bits;

Fig. 3 is a relationship diagram of the variation of the feasible domains of the two cooperation modes with the distance from the user to the base station of the local cell and the base station of the adjacent cell under different transmission signal-to-noise ratios.

Detailed ways

The present invention will be further described below in conjunction with the accompanying drawings.

As shown in Figure 1, a delayed feedback-based multi-cell adaptive cooperative transmission method of the present invention is implemented in the following steps:

1) The system surveys the average moving speed v of multiple user terminals in the M adjacent cells participating in the cooperation, 2≤M≤7, calculates the user's Doppler frequency offset f _d , and determines the channel delay correlation coefficient;

2) Each cell selects a user to wait for data transmission through round-robin scheduling. At the beginning of each transmission, the user first performs channel estimation to obtain channel information and path power attenuation factor, and then quantizes the channel information according to the existing codebook, and Feedback the quantized channel information and path power attenuation factor to the base station;

3) According to the feedback channel information, path power attenuation factor and Doppler frequency offset and other information, the base station calculates the achievable transmission rate of the system in the CBF cooperation mode and the JP cooperation mode respectively, and compares them, and selects the larger mode as the transmission rate model;

的第j列，4) The base station calculates the precoding matrix W of the base station by using the delayed feedback channel information according to the selected transmission mode. If the selected mode is the CBF cooperative mode, the precoding matrix of base station j is

column j of

表示伪逆，

表示基站j到M个用户的反馈信道信息，2≤M≤7；若所选模式为JP协作模式，则基站j的预编码矩阵为基站j到用户k的反馈信道信息

各基站的预编码矩阵确定之后，将待发送数据乘以预编码矩阵W，进行载波调制并发送；in

represents the pseudo-inverse,

Indicates the feedback channel information from base station j to M users, 2≤M≤7; if the selected mode is JP cooperation mode, the precoding matrix of base station j is the feedback channel information from base station j to user k

After the precoding matrix of each base station is determined, the data to be transmitted is multiplied by the precoding matrix W, and the carrier is modulated and sent;

5) The user receives the signal and demodulates it to obtain the final required data information.

Figure 2 is a diagram of the relationship between the feasible domain of the two cooperation modes and the change of the transmission SNR and Doppler frequency offset under different feedback bit conditions. It can be seen from it that when the Doppler frequency offset is large, the transmission SNR When it is very large or small, the performance of the JP cooperative mode is better, and at the same time, the increase of the number of feedback bits can expand the feasible region of the CBF cooperative mode.

Figure 3 is a graph showing the variation of the feasible domains of the two cooperation modes with the distance from the user to the base station of the local cell and the base station of the adjacent cell under different transmission signal-to-noise ratios. It can be seen that when the distance from the user to the base station of the local cell is small, When the distance to the adjacent cell base station is large, the performance of the CBF cooperative mode is better. At the same time, the increase of the transmission signal-to-noise ratio can expand the feasible area of the CBF cooperative mode.

The above is only a preferred embodiment of the present invention, it should be pointed out that for those of ordinary skill in the art, without departing from the principle of the present invention, some improvements and modifications can also be made, and these improvements and modifications are also possible. It should be regarded as the protection scope of the present invention.

Claims (1)

1. A multi-cell adaptive cooperative transmission method based on delayed feedback, characterized in that: the transmission method is carried out in the following steps: (1) Investigate the average mobile velocity v of multiple user terminals in the M adjacent cells participating in the cooperation, 2≤M≤7, calculate the user's Doppler frequency offset f _d =f _c v/c, according to the Clarke scattering model Calculate the channel delay correlation coefficient ρ=J ₀ (2πf _d T _s ), where c represents the speed of light, f _c represents the carrier frequency, T _s represents the length of each symbol period, and J ₀ (.) represents the first type zero order Bessel function; (2) Each cell selects a user to wait for data transmission through round-robin scheduling. At the beginning of each transmission, the user first performs channel estimation to obtain channel information and path power attenuation factor, and then quantizes the channel information according to the existing codebook. Feedback the quantized channel information and the path power attenuation factor to the base station; (3) The base station compares the two alternative modes, the cooperative beamforming mode and the joint processing mode, according to the feedback channel information, path power attenuation factor and Doppler frequency offset, and determines the cooperative transmission mode adopted by the system; Based on the analysis of the non-ideal factors such as quantization error, feedback delay and path power loss in the actual system, the closed-form solutions of the system's achievable transmission rate in the cooperative beamforming mode and the joint processing mode are respectively given R _CBF and R _JP , and based on the closed-form solution, adaptively select the cooperation mode for data transmission: (3-1) Calculate the achievable transmission rates R _CBF and R _JP of the system in the cooperative beamforming mode and the joint processing mode, respectively, 1) In the cooperative beamforming mode, the closed-form solution of the achievable transmission rate R _CBF of the system is: ${\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; CBF</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; M\; lo</span>}{\mathrm{<span\; class="notranslate">\; g</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; e</span>}<span\; class="notranslate">\; )</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}}{\overset{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}<span\; class="notranslate">\; [</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; )</span>}\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; !</span>{<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; \&mu;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{{\mathrm{<span\; class="notranslate">\; \&mu;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; \&mu;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}<span\; class="notranslate">\; ,</span>\frac{{\mathrm{<span\; class="notranslate">\; \&mu;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{{\mathrm{<span\; class="notranslate">\; \&mu;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span>$ In the formula, μ ₁ =αP/M, μ ₂ =βP/M,

Among them, P represents the total transmission power of M base stations, 2≤M≤7, α and β represent the path power attenuation factors from the base station to the users in this cell and users in adjacent cells, respectively, B represents the number of feedback bits, and N _t represents each base station The number of transmitting antennas, N _t ≤ 8,

ρ represents the channel delay correlation coefficient, and at the same time, ${\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; !</span>}{<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}\frac{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; !</span>}{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; !</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; !</span>}{<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; i</span>}}$ ${\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; !</span>}{<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}\frac{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; !</span>}{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; !</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; !</span>}{<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; i</span>}}$ The closed-form solution of I(·,·,·) is given by: $\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 1,1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{<span\; class="notranslate">\; (</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; )</span>}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$ where I ₀ (·,·,·) is given by: ${\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\left\{\begin{array}{cc}{\mathrm{<span\; class="notranslate">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; ab</span>}}{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; ab</span>}<span\; class="notranslate">\; )</span>& \mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>\\ \frac{{<span\; class="notranslate">\; (</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; !</span>}{\mathrm{<span\; class="notranslate">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; ab</span>}}{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; ab</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\frac{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; !</span>{<span\; class="notranslate">\; (</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; !</span>{\mathrm{<span\; class="notranslate">\; b</span>}}^{\mathrm{<span\; class="notranslate">\; k</span>}}}& \mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; \&Greater\; Equal;</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; .</span>\end{array}\right.$ In the formula

is the first-order exponential integral function; 2) In the joint processing mode, the closed-form solution of the achievable transmission rate R _JP of the system is: ${\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; JP</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; log</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&gamma;l</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; ln</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; l</span>}}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; 3</span>}\mathrm{<span\; class="notranslate">\; l</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; 15</span>}{\mathrm{<span\; class="notranslate">\; l</span>}}^{\mathrm{<span\; class="notranslate">\; 4</span>}}}<span\; class="notranslate">\; )</span>$ γ and l are given by: $\mathrm{<span\; class="notranslate">\; \&gamma;</span>}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 2</span>}{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}$ In the formula, ${\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}{\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}{\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}$ A ₂ =1+c ₁ N _t +c ₂ +c ₃ (M-1)N _t +c ₄ (M-1) Among them, c ₁ , c ₂ , c ₃ , and c ₄ are the corresponding constant correction items, and the calculation formula is as follows: ${\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; \&alpha;\&zeta;P</span>}}{\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; \&alpha;P</span>}}{\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}$ ${\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; \&beta;\&zeta;P</span>}}{\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; \&beta;P</span>}}{\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}$ In the formula, $\mathrm{\&zeta;}=1-2^B\&Center\; Dot;\mathrm{\&beta;}(2^B,\frac{N_t}{N_t-1}),$ in, $\mathrm{\&beta;}(x,\mathrm{the\; y})={\&Integral;}_0^1{t}^{x-1}{(1-t)}^{\mathrm{the\; y}-1}\mathrm{dt},$ is the beta function; (3-2) If R _CBF ≥ R _JP is satisfied, then select the cooperative beamforming mode. In this mode, the precoding matrix W of base station j is

The jth column of , where represents the pseudo-inverse,

Indicates the feedback channel information from base station j to M users, 2≤M≤7; If R _JP >R _CBF is satisfied, the joint processing mode is selected. In this mode, the precoding matrix W of base station j is

in

Indicates the feedback channel information from base station j to user k; (4) According to the selected transmission mode, the base station uses the delayed feedback channel information to calculate the precoding matrix W, and then Afterwards, the data to be sent is multiplied by the precoding matrix W for data transmission.

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